The X and Y angles created by lines intersection in the pictures are 18° and 54°.
Based on the picture, angle ∠MON is a right angle hence it has an 90° angle. We then know that the ∠MOA is 72°. Because angle ∠MOA lies within the angle ∠MON, hence we can write the following formula:
∠MON = ∠MOA +∠AON = 90°
∠MON = 72° + ∠AON = 90°
∠AON = 18° ... (i)
If we focus on the line CD being intersected by the line AB, hence we can conclude that the angles form by this intersection will follow these rules:
∠AOD = ∠BOC
∠AOC = ∠BOD
∠AOD + AOC = 180°
∠BOC + ∠BOD = 180°
Based on the picture, we know that:
∠BOC = x
∠AOC = ∠MOA + ∠MOC
∠AOC = 72° + y ...(ii)
∠AOD = ∠AON + ∠NOD
∠AOD = 18° +2x
∠BOC = 3x ... (iii)
Because we already know that ∠BOC = AOD, hence we could rewrite the formula into:
∠BOC = ∠AOD
3x = 18° + 2x
x = 18° ... (iv)
To find the value of y, we need to focus on angle ∠AOC. Based on the previous calculations and formulas, we know that:
∠AOC + ∠BOC = 180° ... (v)
Input equations (ii) and (iv) into (v)
∠AOC + ∠BOC = 180°
(72° + y) + 3x = 180°
72° + y + 3(18°) = 180°
126° + y = 180°
y = 54° ... (vi)
Learn more about the angles by lines intersection here: brainly.com/question/2077876?referrer=searchResults
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Answer:
one real solution
Step-by-step explanation:
it has only one solution since it is a linear graph and only intercepts the x axis once
Answer:
6
Step-by-step explanation:
Answer:
6750
Step-by-step explanation:
simple interest = P×r%×t
P = $6000
r = 2.5%
t = 5 years
I = 6000 × 2.5/100 × 5
= 750
6000 + 750 = $6750
Answer:
∠S = 19°
Step-by-step explanation:
Since all angles in a triangle add up to 180°, we must first find how much is left.
<em>180 - 142 = 38</em>
And since we know that the two lines are congruent, we know that the two other angles will be the same. So we divide the remaining by 2
<em>38 ÷ 2 = 19</em>
So both other angles are 19° meaning that ∠S is 19°
Hope this was helpful!
